The 27-year-old has signed a three-year deal at Hillsborough, becoming the Owls' third signing of the summer as they continue their rebuild under new owners Arise Capital Partners.
Slattery began his career in Chelsea's academy before spells with Southampton, Dutch side De Graafschap and Gillingham.
"This is such an exciting move at an exciting time for the club. I had options, but ultimately when I knew Sheffield Wednesday were interested, it was an easy decision for me to make,” he told Wednesday’s website.
"It's massive. The ambition is there and we want to be positive throughout the whole season. A club this size with that ambition, it's just great to be a part of.
"It's a clean slate for everyone, and to be joining as a new player and a new feeling around the club, it's special.
"Out there on the pitch, I'll be 110% all the time, every chance I get. I want to make things happen, be creative and help the team go in the right direction."